Local Expansions of Solutions of the Fifth Painlevé Equation

The article is devoted to the study of the fifth Painlevé equation. The aim of the present work is to find all asymptotic expansions of solutions of the equation when $x \to 0$. We do this by means of Power Geometry. 27 families of expansions are obtained. 19 of them are obtained from the corresponding expansions of solutions of the sixth Painlevé equation. One of the rest expansions has been already known, one more can be obtained from the expansion of solution of the third Painlevé equation. We have obtained the following new expansions: 3 families of halfexotic expansions, 2 families of complicated expansions and one family of power-logarithmic expansions.